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An object moving at speed 40cm/sec towards a concave mirror of focal kenght 20cm.When the object is at distance 60cm,the speed of image is

An object moving at speed 40cm/sec towards a concave mirror of focal kenght 20cm.When the object is at distance 60cm,the speed of image is
 

Grade:12th pass

1 Answers

Piyush Kumar Behera
435 Points
2 years ago
\frac{1}{f}=\frac{1}{u}+\frac{1}{v}
Differentiating the expression w.r.t. time
0=\frac{1}{v^{2}}\frac{du}{dt}+\frac{1}{u^{2}}\frac{dv}{dt}
\frac{dv}{dt}=-\frac{v^{2}}{u^{2}}\frac{du}{dt}
 
Just find the final position of the image by using the mirror formula...
\frac{1}{-20}=\frac{1}{-60}+\frac{1}{v}
 
Solving we get
v = – 30 cm
 
Now using this formula we get
\frac{dv}{dt}=-\frac{v^{2}}{u^{2}}\frac{du}{dt}
\frac{dv}{dt}=-\frac{(-30)^{2}}{(-60)^{2}} *40
 
\frac{dv}{dt}=-\frac{1}{4}*40
\frac{dv}{dt}=-10 cm/sec
 
So the velocity of the image is 10 cm/sec opposite to the direction of the velocity of object.
 
Piyush Kumar Behera
IIT Dhanbad
 
 

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